Five-dimensional gravity with time-dependent warp factor
This paper has been withdrawn by the authors.
gr-qc↗
arXiv subjects
Pinaki Bhattacharya
Publications and source records attributed to Pinaki Bhattacharya.
Five-dimensional warped product space-time with time-dependent warping and a scalar field in the bulk
We have considered gravity in a five-dimensional warped product space-time, with a time-dependent warp factor and a time-dependent extra dimension. The five-dimensional field equations are derived for a spatially flat FRW brane and the energy conditions and the nature of bulk geometry have been examined. It is found that the expansion of the four-dimensional universe depends on its location along the extra dimension and will be different at different locations in the bulk spacetime. At low energies, the trapping of fields within the brane implies a specific correlation between the warp factor and the extra-dimensional scale factor. Generally, the bulk is not conformally flat. At high energies, the bulk is assumed to be sourced by a scalar field with self-interaction. The analysis shows that the potential of the scalar field source of gravity at a given position along the fifth dimension, is related to the Hubble parameter on the brane at that position in the bulk.
gr-qc↗
Particle Motion and Perturbed Dynamical System in Warped Product Spacetimes
In this paper we have used the dynamical systems analysis to study the dynamics of a five-dimensional universe in the form of a warped product spacetime with a spacelike dynamic extra dimension. We have decomposed the geodesic equations to get the motion along the extra dimension and have studied the associated dynamical system when the cross-diagonal element of the Einstein tensor vanishes, and also when it is non-vanishing. In the first case, introducing the concept of an energy function along the phase path in terms of the extra-dimensional coordinate, we have examined how the energy function depends on the warp factor. The energy function has been used as a measure of the amount of perturbation caused by a brane displacement. Geometrically the effect of brane displacement is manifested in terms of a coordinate translation along the extra dimension, thereby producing a change in the geodesic motion along the extra dimension in the region close to the brane. Then we studied the geodesic motion under a conventional metric perturbation in the form of homothetic motion and conformal motion and examined the nature of critical points for a Mashhoon-Wesson-type metric. Finally we investigated the motion for null and timelike geodesics under the condition when the cross-diagonal element of the Einstein tensor is non-vanishing and examined the effects of perturbation on the critical points of the dynamical system.
gr-qc↗
Confinement and stability of dynamical system in presence of scalar fields and perturbation in the bulk
In this paper we have considered a five-dimensional warped product spacetime with spacelike extra dimension and with a scalar field source in the bulk. We have studied the dynamics of the scalar field under different types of potential in an effort to explain the confinement of particles in the five-dimensional spacetime. The behavior of the system is determined from the nature of damping force on the system. We have also examined the nature of the effective potential under different circumstances. Lastly we have studied the system to determine whether or not the system attains asymptotically stable condition for both unperturbed and perturbed conditions. The analysis throws significant light on the nature confinement of particles and the stability of the dynamical system under these conditions.
gr-qc↗
Particle motion in the field of a five-dimensional charged black hole
In this paper, we have investigated the geodesics of neutral particles near a five-dimensional charged black hole using a comparative approach. The effective potential method is used to determine the location of the horizons and to study radial and circular trajectories. This also helps us to analyze the stability of radial and circular orbits. The radius of the innermost stable circular orbits have also been determined. Contrary to the case of massive particles for which, the circular orbits may have up to eight possible values of specific radius, we find that the photons will only have two distinct values for the specific radii of circular trajectories. Finally we have used the dynamical systems analysis to determine the critical points and the nature of the trajectories for the timelike and null geodesics.
gr-qc↗
Models of Gravity in Five-dimensional Warped Product Spactimes
In this paper, we have considered gravity in a 5-dimensional warped product space-time with a time-dependent warp factor, time-dependent extra dimension and a bulk cosmological constant. The braneworld is described by a spatially flat FRW-type metric. The five-dimensional field equations have been constructed and solved for various cases of the warp factor and the extra-dimensional scale factor, starting from very general type of the metric and then reducing down to specific cases. In the low energy regime, a stabilized bulk with constant curvature has been considered, from which the cosmological behavior of the corresponding observed universe has been interpreted. In the high energy regime, the bulk is assumed to be sourced by an ordinary massless scalar field and thereafter the type of the scalar field source and the different scale factors have been investigated.
gr-qc↗
The critical Reynolds number of a laminar mixing layer
It has hitherto been widely considered that a mixing layer is unstable at all Reynolds numbers. However this is untenable from energy considerations, which demand that there must exist a non-zero Reynolds number below which disturbances cannot extract energy from the mean flow. It is shown here that a linear stability analysis of similarity solutions of the plane mixing layer, including the effects of flow non-parallelism, using the minimal composite theory and the properties of adjoints following Govindarajan & Narasimha (2005), resolves the issue by yielding non-zero critical Reynolds numbers for coflowing streams of any velocity ratio. The critical Reynolds number so found, based on the vorticity thickness and the velocity differential as scales, varies in the narrow range of 59 to 55 as the velocity ratio goes from zero to unity.
physics.flu-dyn↗